Abstract
Following recent evidence that the vortices in decaying two-dimensional turbulence can be classified into small--mobile, and large--quasi-stationary, this paper examines the evidence that the latter might be considered a `crystal' whose formation embodies the inverse cascade of energy towards larger scales. Several diagnostics of order are applied to the ostensibly disordered large vortices. It is shown that their geometric arrangement is substantially more regular than random, that they move more slowly than could be expected from simple mean-field arguments, and that their energy is significantly lower than in a random reorganisation of the same vortices. This is traced to screening of long-range interactions by the preferential association of vortices of opposite sign, and it is argued that this is due to the mutual capture of corrotating vortices, in a mechanism closer to tidal disruption than to electrostatic screening. Finally, the possible relation of these `stochastic crystals' to fixed points of the dynamical system representation of the turbulent flow is briefly examined.
Highlights
This paper is part of a sequence that began as an investigation on whether an automatic computer search of relevant features in decaying two-dimensional turbulence could be used to suggest new ideas about the organization of the flow [1]
Two-dimensional turbulence is a well-studied phenomenon, often used as an approximation to geophysical and stratified flows in which isotropy is broken by some constraint along the third dimension
Much of its theoretical interest can be traced to the early observation in [10] that a system of point vortices in a plane could lead, under some conditions, to states of negative temperature and to the formation of large-scale structures
Summary
This paper is part of a sequence that began as an investigation on whether an automatic computer search of relevant features in decaying two-dimensional turbulence could be used to suggest new ideas about the organization of the flow [1]. It was speculated in [4] that the slowly moving vortex dipoles that flank the jets form a large-scale collective structure that can approximately be described as a crystal and it was further speculated that the formation of the dipoles responds to a tendency of the flow to organize into low-energy configurations This will be shown below to be the case, even if it may be considered counterintuitive in a system, like two-dimensional turbulence, which dissipates enstrophy rather than energy and in which the latter could be expected to lag behind the decay of the former.
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